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Counting passwords made up of letters, digits, and special characters. info About Consider the following definitions for sets of characters: Digits = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 } Letters = { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z } Special characters = { *, &, $, # } Compute the number of passwords that satisfy the given constraints. (a) Strings of length 6. Characters can be special characters, digits, or letters. (b)

User Igneosaur
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Question Continuation

(a) Strings of length 6. Characters can be special characters, digits, or letters, with no repeated characters

(b) Strings of length 6. Characters can be special characters, digits, or letters, with no repeated characters. The first character can not be a special character

Answer:

(a) Number of selection = 2,763,633,600 ways

(b) Number of selection = 2,487,270,240 ways

Explanation:

Number of digits = 10

Letters = 26

Special Characters = 4

Total = 40

(a) Strings of length 6. Characters can be special characters, digits, or letters, with no repeated characters

Since there's no repetition and restrictions of characters

There are 40 ways of selecting the first character

There are 39 ways of selecting the second character

There are 38 ways of selecting the third character

There are 37 ways of selecting the fourth character

There are 36 ways of selecting the fifth character

There are 35 ways of selecting the sixth character

So, there are 40*39*38*37*36*35 ways of selecting a string of 6 characters

Number of selection = 2,763,633,600 ways

(b) Strings of length 6. Characters can be special characters, digits, or letters, with no repeated characters. The first character can not be a special character

Since there's no repetition and restrictions of characters and the first character must not be a special character

There are 36 ways of selecting the first character

There are 39 ways of selecting the second character

There are 38 ways of selecting the third character

There are 37 ways of selecting the fourth character

There are 36 ways of selecting the fifth character

There are 35 ways of selecting the sixth character

So, there are 36*39*38*37*36*35 ways of selecting a string of 6 characters

Number of selection = 2,487,270,240 ways

User Nils Wasell
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